Prime factorization of $$$2300$$$

Find the prime factorization of $$$2300$$$.

Start with the number $$$2$$$.

Determine whether $$$2300$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2300$$$ by $$${\color{green}2}$$$: $$$\frac{2300}{2} = {\color{red}1150}$$$.

Determine whether $$$1150$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1150$$$ by $$${\color{green}2}$$$: $$$\frac{1150}{2} = {\color{red}575}$$$.

Determine whether $$$575$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$575$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$575$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$575$$$ by $$${\color{green}5}$$$: $$$\frac{575}{5} = {\color{red}115}$$$.

Determine whether $$$115$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$115$$$ by $$${\color{green}5}$$$: $$$\frac{115}{5} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$2300 = 2^{2} \cdot 5^{2} \cdot 23$$$.

The prime factorization is $$$2300 = 2^{2} \cdot 5^{2} \cdot 23$$$A.